Ah yes, quite a diabolical room. I'll give you some hints about my approach, and if you're still stuck I can provide more specific help. (You can also post replays of your attempts, if you want to know whether you're on the right track.) There are multiple ways to solve this, but you have to be very careful to avoid getting too many pieces stuck together prematurely.
Box up the bear, by capturing him within the three lower left pieces.
Stash the upper left pieces together into that corner. You can do this in a way that allows you to move the other pieces around.
You need to save a bunch of "L" pieces for the end, which means that you have to clear space for the leftmost square to move past. If you assembled the top corner properly, you have enough room to clear a corridor.
Build a 2-square-high "girder" across the bottom of the board. Notice how the pieces near the bottom center can fit together. You must move the center square out of the way to build this.
Hey folks, GREAT game.  I love the speed at which it moves (if only I weren't such a sloppy clicker ((Heart-felt-thank-you for the r-click-undo)) and patience level down to zero), but I am just not following the hints for H32.  While I'm great at doing Pentominos (aka Tetris-type puzzles) I got sick of the odd shapes in H38 (cheated by using post) and H32 is damn near driving me insane.  It also happens to the last one needing a solution.  Could anyone please, Please, PLEASE, post the solution. (That is: I have not yet seen it in these forums)
Thanks in advance
Apologies in advance for the tone in this post.  I'm miffed beyond belief.
To Gray: Thank you for that solution.
To Weedhopper: When compared to Gray's solution, the hints are worthless.  They ended up confusing me more than helping.  The 3UL becomes 4, then 10-ish.  Boxing the bear was off by one square because of the 3UL...and so the confusion escalated.
To the creator of that disaster: In CC2, please leave out ANYthing that has such a high level of conplexity.  H37 was a chore (an embarrassing 300+ moves) and the pinks were an obstacle, but it was fun to do...like playing with sand.  H25 was a serious pain to me because of the rack of pinks, but at least each 'oops' brought me closer to the solution.  In H32, there is no way to tell if there was an 'oops' until it was FAR FAR FAR too late to figure out what exactly went wrong.  Way too many variables packed too tightly in punishments for being wrong.  Converting a few of the Tans to Blues would have eased the burden j-u-s-t enough.  IMO, H32 is the one bad apple that spoiled the whole bunch.
Okay!  Rant is over.  Thanx for listening.
The sadistic puzzle designer in me has only one thing to say..
* twiddles fingers in a steeple position *
But, yes. H32 annoyed me for the same kind of reasons while I was making it. That's an interesting design principle you've hit upon -  it should be possible to gradually discover things by making mistakes as in H25. If the only reward for making a mistake is that you get to shuffle blocks around for a while before discovering that it was, indeed, a mistake - that's no fun. I was satisfied to eventually find a method I could use to solve H32 (the 2 high slab across the bottom thing), but even if you already have that idea, it takes a fair amount of undirected trial and error.
Lexaloffle: Even though it was the last one I solved (well after I'd mastered most of the other levels), it didn't really annoy me. The satisfaction of 100-percenting the game on such a devious note was great. Now, if I hadn't been able to progress beyond this room and tackle the remaining 7 puzzles first, THAT would have pissed me off mightily.
I didn't particularly like this level at first, too, mostly because it's one of those "tiny space filled with lots of sticky things" levels. Once I got to really trying to optimize my initial 80+ move solution, though, it became kind of fun to find new ways of solving it. I remember actually deciding to publish my score, but then returning to the level and improving it about 3 times.
I must say, I read Weedhopper's hints beforehand and found them useful, even though I wasn't really able to reproduce what they described :) As I was approaching 35 moves, I realized at some point that I was on a completely different track.
I think it's pretty cool that our solutions are so very different. Another proof that the game and the puzzles are really well-designed.